An explicit method for convection-diffusion equations
Copyright policy )An explicit method for convection-diffusion equations
The authors approximate convection-diffusion equations with dominant convection by discretizing in space with piecewise linear finite elements combining with a non-standard explicit Euler scheme for the time integration. They prove that the numerical solution is stable in the \(L^\infty\)-norm in both space and time. Under some conditions they prove also the convergence of the approximations in the maximum norm for any space dimension. Some numerical examples are tested to illustrate the schemes.
- UNIVERSIDADE DE SAO PAULO Brazil
- University of Paris France
- University of Paris France
- Universidade Federal Fluminense Brazil
- University of Brasília Brazil
stable, numerical examples, convergence, diffusion, explicit, explicit Euler scheme, stability, convection-diffusion equations, time-dependent, Finite difference methods for initial value and initial-boundary value problems involving PDEs, finite elements, Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs, Péclet number, Initial value problems for second-order parabolic equations, Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs, convection
stable, numerical examples, convergence, diffusion, explicit, explicit Euler scheme, stability, convection-diffusion equations, time-dependent, Finite difference methods for initial value and initial-boundary value problems involving PDEs, finite elements, Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs, Péclet number, Initial value problems for second-order parabolic equations, Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs, convection
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